3260 Definite Integrals (simple) 



Tabulation of log sin ^. Lindman, C. F. 



Ups. S. Sc. N. Acta 14 (1891) No. I, 15 pp. 

 Theorem. Ramus, C. Crelle J. 24 (1842) 257-. 

 . Grunert, J. A. Grunert Arch. 7 (1846) 



358-. 

 .attempt at proof. Mittag-Leffler,G. Stockh. 



Ofv. 30 (1873) (No. 8) 35-. 



of Cebysev. Usov, N. A. (xn) Eec. Mth. 

 (Moscou) 2 (1867) (Ft. 2) 93-. 



, demonstration. Franklin, F. Am. J. 



Mth. 7 (1885) 377-. 



on integral / <f>(x}.^ (x) dx. Korkine, 



A. G. E. 96 (1883)326-. 

 Theorems. Winckler, A. Wien SB. 21 (1856) 



389-. 

 . Gegenbauer, L. Wien Ak. Sb. 97 (1889) 



(Ab. 2a) 1053-. 

 , connection. Walton, W. [1872] QJ. Mth. 



12 (1873) 126-. 



of Liouville, demonstrations. Glaisher, 

 J.W.L. Mess. Mth. 4 (1875) 170-. 



, generalisation. Rawson, E. Mess. 



Mth. 5 (1876) 30-. 

 Theory. Schlomilch, 0. Grunert Arch. 1 



(1841) 417-. 

 . Grunert, J. A. Grunert Arch. 2 (1842) 



266-; 4 (1844) 113-. 



(Grunert). Meyer, U. H. Grunert Arch. 5 

 (1844) 216-. 



. Russell, W. H. L. [1854] Phil. Trans. 



(1855) 157-. 



. [Bierens de] Haan, D. Amst. Vs. Ak. 4 



(1856) 332- ; 16 (1864) 28- ; 1 (1866) (Ntk.) 

 117- ; 3 (1869) (Ntk.) 323- ; 5 (1871) (Ntk.) 

 65-; 7 (1873) 12-; Arch. Neerl. 2 1867) 

 349-. 



. Enneper, A. Schlomilch Z. 6 (1861) 289-. 

 . Gomes Teixeira, F. G. Teix. J. Sc. 9 



(1889) 39-; Fschr. Mth. (1889) 276. 

 . Schiff, P. Eec. Mth. (Moscou) 17 (1895) 



607- ; Fschr. Mth. (1895) 321-. 

 , elementary. Meyer, A. Liege Mm. S. Sc. 



7 (1851) 510 pp. 

 , formulae. Cauchy, A. L. [1815] Par. EC. 



Pol. J. 28 cah. (1841) 147-. 

 , . Andreiewsky,. Mth. A. 4 (1871)550-. 

 , foundations. Haan, D. Bierens de. Amst. 



Arch. Wisk. Gn. 1 (1856-59) 343-. 

 Transcendents, functional, reduction. Glaisher, 



J. W. L. Mess. Mth. 1 (1872) 153-. 

 , squares of. Pendlebury, R. [1871] Mess. 



Mth. 1 (1872) 131-. 



Transformation. 



Bassani, A. G. Mt. 25 (1887) 223-. 

 Nielsen, N. Kjrfb. Ov. (1896) 335-. 

 Kapteyn, W. N. Arch. Wisk. 4 (1899) 243-. 

 and calculation. Blatek, G. [1864] Wien Sb. 



50 (1865) (Ab. 2) 60-. 

 cases. Schaar, M. Brux. Ac. Bll. 13 (1846) 



(pte. 2) 30-. 



. Schlomilch, 0. Crelle J. 36 (1848) 271-. 

 . Hoppe, R. Crelle J. 40 (1850) 139-. 

 . Besge, V. A. Liouv. J. Mth. 18 (1853) 112-. 



Transformation 3260 



cases. SchlGmilch, 0. Leip. B. 9 (1857) 181- ; 

 Schlomilch Z. 3 (1858) 115-. 



. Unferdinger, F. Arch. Mth. Ps. 53 (1871) 

 27-. 



. Glaisher, J. W. L. [1876] Mess. Mth. 6 

 (1877) 155-. 



. Silva, J. A. Martins da. G. Teix. J. Sc. 

 3 (1881) 177-. 



by Cebysev's formula, generalisations. And- 



reev, K. A. (xn) Kharkov Mth. S. Com. 



(1883) 19-. 

 and determination. Cauchy, A. L. C. E. 12 



(1841) 1145-. 

 and evaluation. Haan, D. Bierens de. Amst. 



Vh. 8 (1862) 702 pp. 



formula. Jacobi,C.G.J. Crelle J. 15 (1836) 1-. 

 general. Kummer, E. E. Crelle J. 20 (1840) 



theory. Dirksen, E. H. Berl. B. (1848) 152-. 

 in variation. Sabinin, E. T. [1890] Eec. Mth. 



(Moscou) 15 (1891) 99- ; Fschr. Mth. (1890) 



380. 



of D^ =0 (l-2fccos7 + fc 2 )~i into definite in- 

 tegrals. Dirksen, E.H. Berl. B. (1848) 120-. 



Transition from indefinite to definite integrals. 



Heine, H. E. Crelle J. 51 (1856) 382-. 

 Use of multiform functions in finding definite 



integrals. Raabe, J. L. Crelle J. 37 (1848) 



356-. 



l 1 x n dxe~ axSm fix. Fuss, N. [1810] St Pet. 

 J o cos 



Ac. Sc. Mm. 11 (1830) 238-. 



I e~ x2 dx = ^Jw. Buzengeiger, K. H. J. 

 Zach M. Cor. 24 (1811) 169-. 



i . Frullani, G. Mod. 



S. It. Mm. 19 (1821) 223-. 



* z i dzF(cos z). Frullani, G. Mod. S. It. 



Mm. 20 (1828) 712-. 

 1 x 2m dx cos ax 



Plana, G. [1836] Quetelet Cor. Mth. 9 (1837) 

 47-. 



<f> (sin ax, cos bx) dx, reduction. Raabe, J. L. 

 Crelle J. 15 (1836) 355-. 



<f> (x) dx when <j> (x) is infinite or discon- 

 tinuous. Raabe, J. L. [1837] Crelle J. 20 

 (1840) 173-. 



log (1 - 2a cos x + a 2 ) dx. Delaunay, C. 

 Liouv. J. Mth. 3 (1838) 355-. 

 cos as da Catalan, E.G. Liouv. J. Mth. 



5 (1840) 110-. 



=V, for potential of ellipsoid. Plana, G. 



Crelle J. 20 (1840) 271-. 



280 



